The built-in Limit function only knows about elementary functions
and things for which it can construct power series expansions (no
essential singularities, etc.). The Calculus`Limit` package knows
about a far broader class of functions and uses a more powerful
algorithm.
In[1]:= << Calculus`Limit`
In[2]:= Limit[BesselI[I + eps, 1],eps->0]
Out[2]= BesselI[I, 1]
It is likely that some version of the algorithm used in this package
will eventually be used to extend or replace the built-in code.
David Withoff <withoff at wri.com>